Example 4 solution

Example 4 solution - When source spectral width is...

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(a) When source spectral width is negligible and 2 0 β = , for Gaussian input pulses of rms pulse width 0 σ the rms output pulse width after a transmission length of L is given as: 2 22 2 3 0 2 0 (1 ) 42 L C σσ ⎛⎞ =+ + ⎜⎟ ⎝⎠ . The limitation to the bit rate can be determined using the condition 41 B , where B is the bit rate. We can obtain the maximum bit rate using using this criteria as: max min B = or max min 16 1 B = . Using the previous expression, input rms pulse width and the maximum bit rate are related as: max 2 3 0 2 0 1 4( 1 ) B L C = ++ . The optimum input rms pulse width is found using the condition: max 0 0 dB d = . 2 33 0 23 00 max 3 2 0 2 3 0 2 0 ( 1) 2 1 0 8 ) LL C dB d L C ββ =− = ⎡⎤ ⎢⎥ ⎣⎦ . This yields: 2 ( 1 ) 2 0 opt opt opt C = or 2 62 3 ) 4 opt L C . Then the solution is 1 2 6 2 3 ) 4 opt L C .
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(b) Remember the output pulse width was: 2 22 2 3 0 2 0 (1 ) 42 L C β σσ σ ⎛⎞ =+ + ⎜⎟ ⎝⎠ . Recognizing 2 26 3 ) 4 opt L C ⎡⎤ += ⎢⎥ ⎣⎦ We obtain 2 3
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Example 4 solution - When source spectral width is...

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